import sys
sys.setrecursionlimit(10000)
import warnings
warnings.filterwarnings('ignore', category=DeprecationWarning)

import cPickle
import gzip

from breze.learn.data import one_hot
from breze.learn.base import cast_array_to_local_type
from breze.learn.utils import tile_raster_images

import climin.stops
import climin.initialize

from breze.learn import hvi
from breze.learn.hvi import HmcViModel
from breze.learn.hvi.energies import (NormalGaussKinEnergyMixin, DiagGaussKinEnergyMixin)
from breze.learn.hvi.inversemodels import MlpGaussInvModelMixin

from matplotlib import pyplot as plt
from matplotlib import cm

import numpy as np

#import fasttsne

from IPython.html import widgets
%matplotlib inline

import theano
theano.config.compute_test_value = 'ignore'#'raise'
from theano import (tensor as T, clone)

Couldn't import dot_parser, loading of dot files will not be possible.

//anaconda/lib/python2.7/site-packages/IPython/html.py:14: ShimWarning: The `IPython.html` package has been deprecated. You should import from `notebook` instead. `IPython.html.widgets` has moved to `ipywidgets`.
  "`IPython.html.widgets` has moved to `ipywidgets`.", ShimWarning)

datafile = '../mnist.pkl.gz'
# Load data.                                                                                                   

with gzip.open(datafile,'rb') as f:                                                                        
    train_set, val_set, test_set = cPickle.load(f)                                                       

X, Z = train_set                                                                                               
VX, VZ = val_set
TX, TZ = test_set

Z = one_hot(Z, 10)
VZ = one_hot(VZ, 10)
TZ = one_hot(TZ, 10)

X_no_bin = X
VX_no_bin = VX
TX_no_bin = TX

# binarize the MNIST data
np.random.seed(0)
X  = np.random.binomial(1, X) * 1.0
VX = np.random.binomial(1, VX) * 1.0
TX = np.random.binomial(1, TX) * 1.0

image_dims = 28, 28

X, Z, VX, VZ, TX, TZ = [cast_array_to_local_type(i) for i in (X, Z, VX,VZ, TX, TZ)]
print X.shape

(50000, 784)

print np.array([X_no_bin.sum(0) == 0]).sum()
all_samples = np.append(X_no_bin, VX_no_bin, axis=0)
all_samples = np.append(all_samples, TX_no_bin, axis=0)
print np.array([all_samples.sum(0) == 0]).sum()

#fig, ax = plt.subplots(figsize=(4, 4))
#img = tile_raster_images(np.array([all_samples.sum(0) == 0])*1.0, image_dims, (1, 1), (1, 1))
#ax.imshow(img, cmap=cm.binary)

67
65

fig, ax = plt.subplots(figsize=(9, 9))

img = tile_raster_images(X[:64], image_dims, (8, 8), (1, 1))
ax.imshow(img, cmap=cm.binary)

<matplotlib.image.AxesImage at 0x10763b9d0>

Model setup

fast_dropout = False

if fast_dropout:
    class MyHmcViModel(HmcViModel, 
                   hvi.FastDropoutMlpBernoulliVisibleVAEMixin, 
                   hvi.FastDropoutMlpGaussLatentVAEMixin, 
                   DiagGaussKinEnergyMixin,
                   MlpGaussInvModelMixin):
        pass

    kwargs = {
        'p_dropout_inpt': .1,
        'p_dropout_hiddens': [.2, .2],
    }

    print 'yeah'

else:
    class MyHmcViModel(HmcViModel, 
                   hvi.MlpBernoulliVisibleVAEMixin, 
                   hvi.MlpGaussLatentVAEMixin, 
                   DiagGaussKinEnergyMixin,
                   MlpGaussInvModelMixin):
        pass
    kwargs = {}


batch_size = 200
#optimizer = 'rmsprop', {'step_rate': 1e-4, 'momentum': 0.95, 'decay': .95, 'offset': 1e-6}
#optimizer = 'adam', {'step_rate': .5, 'momentum': 0.9, 'decay': .95, 'offset': 1e-6}
optimizer = 'adam', {'step_rate': 0.001}

# This is the number of random variables NOT the size of 
# the sufficient statistics for the random variables.
n_latents = 2
n_hidden = 200

m = MyHmcViModel(X.shape[1], n_latents, 
                 [n_hidden, n_hidden], ['rectifier'] * 2, 
                 [n_hidden], ['rectifier'] * 1, 
                 [n_hidden], ['rectifier'] * 1,
                 n_hmc_steps=3, n_lf_steps=4,
                 n_z_samples=1,
          optimizer=optimizer, batch_size=batch_size, allow_partial_velocity_update=False, perform_acceptance_step=True,
          **kwargs)

climin.initialize.randomize_normal(m.parameters.data, 0.1, 1e-1)
m.parameters.__setitem__(m.hmc_sampler.step_size_param, 0.01)
#m.parameters.__setitem__(m.kin_energy.mlp.layers[-1].bias, 1)

Loading parameters

old_best_params = None
#print m.score(TX)
print m.parameters.data.shape

(514595,)

FILENAME = 'hvi_gen2_recog1_aux1_late2_hid200_fullbin_untrained.pkl'

# In[5]:
#old_best_params = None
f = open(FILENAME, 'rb')
np_array = cPickle.load(f)
old_best_params = cast_array_to_local_type(np_array)
f.close()
print old_best_params.shape

(514595,)

m.parameters.data = old_best_params.copy()
#old_best_loss = m.score(VX)

Model performance

print m.score(VX)
print m.score(TX)

144.0980625
145.8428125

print m.parameters.view(m.init_recog.mlp.layers[1].bias)

[ 0.05071862 -0.16010898 -5.13858843 -7.01162291]

m.parameters.__setitem__(m.hmc_sampler.step_size_param, 0.2)
m.parameters.__setitem__(m.kin_energy.variance_parameter, np.array([0.7, 0.7]))
#m.parameters.__setitem__(m.init_recog.mlp.layers[1].bias, np.array([0.05071862, -0.16010898, -2.13858843, -4.01162291]).astype('float32'))

print 0.1 * m.parameters.view(m.hmc_sampler.step_size_param) ** 2 + 1e-8

[ 0.00400001]

#print m.estimate_nll(TX, 500)

print m.score(VX_no_bin)
print m.score(TX_no_bin)

Model training

max_passes = 250
max_iter = max_passes * X.shape[0] / batch_size
n_report = X.shape[0] / batch_size

stop = climin.stops.AfterNIterations(max_iter)
pause = climin.stops.ModuloNIterations(n_report)

# theano.config.optimizer = 'fast_compile'

for i, info in enumerate(m.powerfit((X_no_bin,), (VX,), stop, pause, eval_train_loss=False)):
    print i, info['loss'], info['val_loss']
    if i == 0 and old_best_params is not None:
        if info['best_loss'] > old_best_loss:
            info['best_loss'] = old_best_loss
            info['best_pars'] = old_best_params
    
    if info['best_loss'] == info['val_loss']:
        np.savetxt('hvi_short_basic_test.csv', m.parameters.data, delimiter=',')

Function definitions

f_z_init_sample = m.function(['inpt'], m.init_recog.sample())
f_z_sample = m.function(['inpt'], m.hmc_sampler.output)
f_gen = m.function([m.gen.inpt], m.gen.sample())
f_gen_rate = m.function([m.gen.inpt], m.gen.rate)

curr_pos = T.matrix('current_position')
curr_vel = T.matrix('current_velocity')
norm_noise = T.matrix('normal_noise')
unif_noise = T.vector('uniform_noise')

new_sampled_vel = m.hmc_sampler.kin_energy.sample(norm_noise)
updated_vel = m.hmc_sampler.partial_vel_constant * curr_vel + m.hmc_sampler.partial_vel_complement * new_sampled_vel
performed_hmc_steps = m.hmc_sampler.perform_hmc_steps(curr_pos, curr_vel)
hmc_step = m.hmc_sampler.hmc_step(curr_pos, curr_vel, np.float32(0), norm_noise, unif_noise)
lf_step_results = m.hmc_sampler.simulate_dynamics(curr_pos, curr_vel, return_full_list=True)

f_pot_en = m.function(['inpt', curr_pos], m.hmc_sampler.eval_pot_energy(curr_pos))
f_kin_en = m.function(['inpt', curr_vel], m.kin_energy.nll(curr_vel).sum(-1))
f_perform_hmc_steps = m.function(['inpt', curr_pos, curr_vel], 
                                T.concatenate([performed_hmc_steps[0], performed_hmc_steps[1]], axis=1))
f_hmc_step = m.function(['inpt', curr_pos, curr_vel, norm_noise, unif_noise], 
                        T.concatenate([hmc_step[0], hmc_step[1]],axis=1), on_unused_input='warn')
f_kin_energy_sample_from_noise = m.function(['inpt', norm_noise], new_sampled_vel)
f_updated_vel_from_noise = m.function(['inpt', curr_vel, norm_noise], updated_vel)
f_perform_lf_steps = m.function(['inpt', curr_pos, curr_vel],
                               T.concatenate([lf_step_results[0], lf_step_results[1]], axis=0))

f_z_init_mean = m.function(['inpt'], m.init_recog.mean)
f_z_init_var = m.function(['inpt'], m.init_recog.var)

f_v_init_var = m.function(['inpt'], m.kin_energy.var)

full_sample = m.hmc_sampler.sample_with_path()
f_full_sample = m.function(['inpt'], T.concatenate([full_sample[0], full_sample[1]], axis=1))

final_pos = T.matrix('final_pos')
final_vel = T.matrix('final_vel')
inpt_replacements = {m.final_vel_model_inpt['position']: final_pos,
                     m.final_vel_model_inpt['time']: T.cast(m.hmc_sampler.n_hmc_steps, dtype='float32')}

final_vel_model_var = clone(m.final_vel_model.var, replace=inpt_replacements)
final_vel_model_mean = clone(m.final_vel_model.mean, replace=inpt_replacements)
final_vel_model_nll = clone(m.final_vel_model.nll(final_vel).sum(-1), replace=inpt_replacements)

f_v_final_var = m.function(['inpt', final_pos], final_vel_model_var)
f_v_final_mean = m.function(['inpt', final_pos], final_vel_model_mean)
f_v_final_model_nll = m.function(['inpt', final_pos, final_vel], final_vel_model_nll)

f_init_recog_nll = m.function(['inpt'], m.init_recog.expected_nll.sum(-1))

print f_init_recog_nll(X).mean()

-7.72047

Visualizations

Comparison of initial recognition model with full HVI model on training samples

Reconstruction of training samples

fig, axs = plt.subplots(2, 3, figsize=(27, 18))

### Original data

O = (X_no_bin[:64])[:, :784].astype('float32')
img = tile_raster_images(O, image_dims, (8, 8), (1, 1))
axs[0, 0].imshow(img, cmap=cm.binary)

O2 = (X[:64])[:, :784].astype('float32')
img = tile_raster_images(O2, image_dims, (8, 8), (1, 1))
axs[1, 0].imshow(img, cmap=cm.binary)

### Reconstruction

#z_sample = f_z_sample((X[:64]))
z_init_sample = f_z_init_sample((X[:64]))
z_sample = f_perform_hmc_steps((X[:64]), 
                               z_init_sample, 
                               f_kin_energy_sample_from_noise((X[:64]), 
                                                              np.random.normal(size=(64, m.n_latent)).astype('float32'))
                               )[-1, :64, :]

R = f_gen_rate(z_sample)[:, :784].astype('float32')
img = tile_raster_images(R, image_dims, (8, 8), (1, 1))
axs[0, 1].imshow(img, cmap=cm.binary)

Rinit = f_gen_rate(z_init_sample)[:, :784].astype('float32')
img = tile_raster_images(Rinit, image_dims, (8, 8), (1, 1))
axs[0, 2].imshow(img, cmap=cm.binary)

R2 = f_gen(z_sample)[:, :784].astype('float32')
img = tile_raster_images(R2, image_dims, (8, 8), (1, 1))
axs[1, 1].imshow(img, cmap=cm.binary)

Rinit2 = f_gen(z_init_sample)[:, :784].astype('float32')
img = tile_raster_images(Rinit2, image_dims, (8, 8), (1, 1))
axs[1, 2].imshow(img, cmap=cm.binary)

<matplotlib.image.AxesImage at 0x11bec1e10>

Generating new data samples

fig, axs = plt.subplots(1, 2, figsize=(18, 9))

prior_sample = np.random.randn(64, m.n_latent).astype('float32')

S = f_gen_rate(prior_sample)[:, :784].astype('float32')
img = tile_raster_images(S, image_dims, (8, 8), (1, 1))
axs[0].imshow(img, cmap=cm.binary)

S2 = f_gen(prior_sample)[:, :784].astype('float32')
img = tile_raster_images(S2, image_dims, (8, 8), (1, 1))
axs[1].imshow(img, cmap=cm.binary)

#S3 = f_gen_rate(prior_sample)[:, :784].astype('float32')
#img = tile_raster_images(S, image_dims, (8, 8), (1, 1))
#axs[2, 2].imshow(img, cmap=cm.nipy_spectral)

<matplotlib.image.AxesImage at 0x119f07550>

Learned data manifold

# TODO: Axis titles, plot title, make this work if one selects two dimensions out of more than two (i.e. if n_latent>2)

from scipy.stats import norm as normal_distribution

unit_interval_positions = np.linspace(0.025, 0.975, 20)
positions = normal_distribution.ppf(unit_interval_positions)
print unit_interval_positions
print positions

latent_array = np.zeros((400, 2))

latent_array[:, 1] = -np.repeat(positions, 20)  # because images are filled top -> bottom, left -> right (row by row)
latent_array[:, 0] = np.tile(positions, 20)
        
fig, axs = plt.subplots(1, 1, figsize=(24, 24))

F = f_gen_rate(latent_array.astype('float32'))

img = tile_raster_images(F, image_dims, (20, 20), (1, 1))
#axs.imshow(img, cmap=cm.nipy_spectral)
axs.imshow(img, cmap=cm.binary)

[ 0.025  0.075  0.125  0.175  0.225  0.275  0.325  0.375  0.425  0.475
  0.525  0.575  0.625  0.675  0.725  0.775  0.825  0.875  0.925  0.975]
[-1.95996398 -1.43953147 -1.15034938 -0.93458929 -0.75541503 -0.59776013
 -0.45376219 -0.31863936 -0.18911843 -0.06270678  0.06270678  0.18911843
  0.31863936  0.45376219  0.59776013  0.75541503  0.93458929  1.15034938
  1.43953147  1.95996398]

<matplotlib.image.AxesImage at 0x12aa02f10>

Latent representation of training set X

L = f_z_sample(X)
L_init = f_z_init_sample(X)

Select dimensions

dim1 = 0
dim2 = 1

fig, axs = plt.subplots(1, 2, figsize=(18, 9))
axs[0].scatter(L[:, dim1], L[:, dim2], c=Z[:].argmax(1), lw=0, s=5, alpha=.2)
axs[1].scatter(L_init[:, dim1], L_init[:, dim2], c=Z[:].argmax(1), lw=0, s=5, alpha=.2)

cax = fig.add_axes([0.95, 0.2, 0.02, 0.6])
cax.scatter(np.repeat(0, 10), np.arange(10), c=np.arange(10), lw=0, s=300)
cax.set_xlim(-0.1, 0.1)
cax.set_ylim(-0.5, 9.5)
plt.yticks(np.arange(10))
plt.tick_params(axis='x', which='both', bottom='off', top='off', labelbottom='off')
cax.tick_params(axis='y', colors='white')
for tick in cax.yaxis.get_major_ticks():
    tick.label.set_fontsize(14)
    tick.label.set_color('black')
    
cax.spines['bottom'].set_color('white')
cax.spines['top'].set_color('white') 
cax.spines['right'].set_color('white')
cax.spines['left'].set_color('white')

axs[0].set_title('After HMC steps')
axs[1].set_title('Initial recognition model')

axs[0].set_xlim(-3, 3)
axs[0].set_ylim(-3, 3)
axs[1].set_xlim(-3, 3)
axs[1].set_ylim(-3, 3)

(-3, 3)

fig, axs = plt.subplots(4, 5, figsize=(20, 16))
colors = cm.jet(np.linspace(0, 1, 10))
for i in range(5):
    axs[0, i].scatter(L_init[Z[:].argmax(1) == i, dim1], L_init[Z[:].argmax(1) == i, dim2], c=colors[i], lw=0, s=5, alpha=.2)
    axs[1, i].scatter(L[Z[:].argmax(1) == i, dim1], L[Z[:].argmax(1) == i, dim2], c=colors[i], lw=0, s=5, alpha=.2)
    axs[0, i].set_title(str(i) + ' before HMC')
    axs[1, i].set_title(str(i) + ' after HMC')
    axs[2, i].scatter(L_init[Z[:].argmax(1) == (5+i), dim1], L_init[Z[:].argmax(1) == (5+i), dim2], c=colors[5+i], lw=0, s=5, alpha=.2)
    axs[3, i].scatter(L[Z[:].argmax(1) == (5+i), dim1], L[Z[:].argmax(1) == (5+i), dim2], c=colors[5+i], lw=0, s=5, alpha=.2)
    axs[2, i].set_title(str(5+i) + ' before HMC')
    axs[3, i].set_title(str(5+i) + ' after HMC')
    for j in range(4):
        axs[j, i].set_xlim(-3, 3)
        axs[j, i].set_ylim(-3, 3)

Sample specific visualizations

Configuration: Select sample

X_index = 3  # index=0 -> 5, index=1 -> 0, index=2 -> 4, index=3 -> 1
num_repeats = 1000

fig, axs = plt.subplots(1, 2, figsize=(6, 3))
img = tile_raster_images(np.array([X[X_index, :]]), image_dims, (1, 1), (1, 1))
axs[0].imshow(img, cmap=cm.binary)
img = tile_raster_images(np.array([X_no_bin[X_index, :]]), image_dims, (1, 1), (1, 1))
axs[1].imshow(img, cmap=cm.binary)

<matplotlib.image.AxesImage at 0x141258890>

repeated_X = np.tile(np.array([X[X_index, :]]), (num_repeats, 1)).astype('float32')

full_sample = f_full_sample(repeated_X)
z_samples = full_sample[:, :num_repeats, :]
v_samples = full_sample[:, num_repeats:, :]

z_sample_final_mean = z_samples[m.n_hmc_steps, :, :].mean(axis=0)
z_sample_final_std = z_samples[m.n_hmc_steps, :, :].std(axis=0)

print 'Posterior distribution statistics'
print
print 'Initial model: - Mean: ' + str(f_z_init_mean(np.array([X[X_index, :]]))[0])
print '               - Var:  ' + str(f_z_init_var(np.array([X[X_index, :]]))[0])
print
print 'Full HVI model: - Mean: ' + str(z_sample_final_mean)
print '                - Var:  ' + str(z_sample_final_std ** 2)
print
print 'Velocity model variance: ' + str(f_v_init_var(np.array([X[X_index, :]]))[0])

Posterior distribution statistics

Initial model: - Mean: [ 0.61576778  1.87005877]
               - Var:  [ 0.00067139  0.00707683]

Full HVI model: - Mean: [ 0.61859483  1.87671542]
                - Var:  [ 0.00087147  0.00687835]

Velocity model variance: [ 2.0137527  2.0137527]

Configuration: Select dimensions

dim1 = 0
dim2 = 1

Energy surfaces

resolution = 201
lower_dim1_limit = z_sample_final_mean[dim1] - 0.2
upper_dim1_limit = z_sample_final_mean[dim1] + 0.2
lower_dim2_limit = z_sample_final_mean[dim2] - 0.2
upper_dim2_limit = z_sample_final_mean[dim2] + 0.2

number_images_per_axis = 11
latent_array = np.zeros((number_images_per_axis**2, 2))
gap_between_images = (resolution - 1)//(number_images_per_axis - 1)
indices_for_images = np.arange(0, resolution, gap_between_images)

pot_energy_matrix = np.zeros((resolution, resolution), dtype='float32')
x = cast_array_to_local_type(np.linspace(lower_dim1_limit, upper_dim1_limit, resolution))
y = cast_array_to_local_type(np.linspace(lower_dim2_limit, upper_dim2_limit, resolution))
for i in range(resolution):
    for j in range(resolution):
        #pos_array = f_z_init_mean(np.array([X[X_index, :]]))
        pos_array = np.array([z_sample_final_mean])
        pos_array[0, dim1] = x[i]
        pos_array[0, dim2] = y[j]
        pot_energy_matrix[j, i] = f_pot_en(np.array([X[X_index, :]]), pos_array)
        if i in indices_for_images and j in indices_for_images:
            latent_array[(i//gap_between_images) + (number_images_per_axis - 1 - j//gap_between_images)*number_images_per_axis , :] = pos_array[0, :]

        
print 'Minimum potential energy (at grid points): ' + str(pot_energy_matrix.min())
print 'Maximum potential energy (at grid points): ' + str(pot_energy_matrix.max())

fig, axs = plt.subplots(1, 2, figsize=(18, 9))
CS = axs[0].contour(x, y, pot_energy_matrix, 20)
plt.clabel(CS, inline=1, fmt='%1.0f', fontsize=10)
axs[0].set_title('Potential energy surface')

F = f_gen_rate(latent_array.astype('float32'))
img = tile_raster_images(F, image_dims, (number_images_per_axis, number_images_per_axis), (1, 1))
#axs.imshow(img, cmap=cm.nipy_spectral)
axs[1].imshow(img, cmap=cm.binary)
plt.show()

Minimum potential energy (at grid points): 49.007
Maximum potential energy (at grid points): 79.8015

resolution = 200
underlying_variance = f_v_init_var(np.array([X[X_index, :]]))
velocity_range_for_images = 10.0 * np.sqrt(underlying_variance[0, :])
lower_dim1_limit = np.around(- velocity_range_for_images[dim1])
upper_dim1_limit = np.around(  velocity_range_for_images[dim1])
lower_dim2_limit = np.around(- velocity_range_for_images[dim2])
upper_dim2_limit = np.around(  velocity_range_for_images[dim2])

kin_energy_matrix = np.zeros((resolution, resolution), dtype='float32')
kin_x = cast_array_to_local_type(np.linspace(lower_dim1_limit, upper_dim1_limit, resolution))
kin_y = cast_array_to_local_type(np.linspace(lower_dim2_limit, upper_dim2_limit, resolution))
for i in range(resolution):
    for j in range(resolution):
        vel_array = np.zeros((1, m.n_latent)).astype('float32')
        vel_array[0, dim1] = kin_x[i]
        vel_array[0, dim2] = kin_y[j]
        kin_energy_matrix[j, i] = f_kin_en(np.array([X[X_index, :]]), vel_array)

print 'Minimum kinetic energy (at grid points): ' + str(kin_energy_matrix.min())
print 'Maximum kinetic energy (at grid points): ' + str(kin_energy_matrix.max())

fig, ax = plt.subplots(1, 1, figsize=(9, 9))
CS = ax.contour(kin_x, kin_y, kin_energy_matrix)
plt.clabel(CS, inline=1, fmt='%1.1f', fontsize=10)
ax.set_title('Kinetic energy surface')
plt.show()

Minimum kinetic energy (at grid points): 2.54033
Maximum kinetic energy (at grid points): 99.8686

Evolution of recognition model distribution with HMC steps

fig, axs = plt.subplots(m.n_hmc_steps + 1, 3, figsize=(18, (m.n_hmc_steps + 1) * 6))
colors = cm.jet(np.linspace(0, 1, 10))

#contour_levels = (198, 200, 202, 204, 206, 208, 210)
#contour_levels = (130, 140, 150, 160, 180, 200, 240, 280)
#contour_levels = (180, 190, 200, 220, 240, 260, 280, 300, 320)
#contour_levels = (400, 402, 404, 406, 408, 410, 412, 416, 420)
#contour_levels = (106, 108, 110, 112, 114, 116, 118, 120, 124, 128)
#contour_levels = (160, 165, 170, 175, 180, 185, 190, 195, 200, 210, 220, 230, 240, 250)
#contour_levels = (174, 175, 176, 177, 178, 180, 182, 184, 186, 190, 200)
contour_levels = (50, 51, 52, 54, 56, 58, 60, 64, 68, 72)
#contour_levels = (59, 61, 63, 65, 67, 69, 71, 73, 75, 80, 85, 90)

vel_contour_levels = np.linspace(2.0, 70.0, 18)
#CS0 = axs[0, 0].contourf(x, y, pot_energy_matrix, np.linspace(155, 240, 500))

def colour_for_z_samples(samples):
    mean = samples.mean(axis=0)
    mean1 = mean[dim1]
    mean2 = mean[dim2]
    colour = np.zeros_like(samples[:, 0])
    colour[np.logical_and(samples[:, dim1] < mean1,  samples[:, dim2] < mean2)] = 0
    colour[np.logical_and(samples[:, dim1] < mean1,  samples[:, dim2] >= mean2)] = 2
    colour[np.logical_and(samples[:, dim1] >= mean1, samples[:, dim2] < mean2)] = 4
    colour[np.logical_and(samples[:, dim1] >= mean1, samples[:, dim2] >= mean2)] = 7
    colour[((samples[:, dim1] - mean1) ** 2 + (samples[:, dim2] - mean2) ** 2) < 1e-5] = 9
    return colour.astype('int32')

colour = colour_for_z_samples(z_samples[m.n_hmc_steps,:,:])
print v_samples[m.n_hmc_steps, colour == 0, :].mean(axis=0)
print v_samples[m.n_hmc_steps, colour == 2, :].mean(axis=0)
print v_samples[m.n_hmc_steps, colour == 4, :].mean(axis=0)
print v_samples[m.n_hmc_steps, colour == 7, :].mean(axis=0)
print v_samples[m.n_hmc_steps, colour == 9, :].mean(axis=0)
print v_samples[m.n_hmc_steps, colour == 0, :].var(axis=0)
print v_samples[m.n_hmc_steps, colour == 2, :].var(axis=0)
print v_samples[m.n_hmc_steps, colour == 4, :].var(axis=0)
print v_samples[m.n_hmc_steps, colour == 7, :].var(axis=0)
print v_samples[m.n_hmc_steps, colour == 9, :].var(axis=0)


for i in range(m.n_hmc_steps + 1):
    CS = axs[i, 0].contour(x, y, pot_energy_matrix, contour_levels)
    plt.clabel(CS, inline=1, fmt='%1.0f', fontsize=10)
    axs[i, 0].scatter(z_samples[i,:,dim1], z_samples[i,:,dim2], c=colors[colour_for_z_samples(z_samples[i,:,:])], s=20, alpha=.3, lw=0)
    
    CS_vel = axs[i, 1].contour(kin_x, kin_y, kin_energy_matrix, vel_contour_levels)
    plt.clabel(CS_vel, inline=1, fmt='%1.1f', fontsize=10)
    axs[i, 1].scatter(v_samples[i,:,dim1], v_samples[i,:,dim2], c=colors[colour_for_z_samples(z_samples[i,:,:])], s=20, alpha=.3, lw=0)
    
    pot_energy_distrib = f_pot_en(repeated_X, z_samples[i, :, :])
    pot_energy_distrib_mean = pot_energy_distrib.mean()
    axs[i, 2].hist(pot_energy_distrib, 50, normed=1, range=(np.floor(pot_energy_matrix.min()), contour_levels[-1]))
    axs[i, 2].axvline(pot_energy_distrib_mean, color='r', linestyle='dashed', linewidth=2)
    axs[i, 2].text(pot_energy_distrib_mean + 1.0, 0.8*axs[i, 2].get_ylim()[1], 'Mean: ' + str(pot_energy_distrib_mean))
    axs[i, 1].set_xlim(-velocity_range_for_images[dim1], velocity_range_for_images[dim1])
    axs[i, 1].set_ylim(-velocity_range_for_images[dim2], velocity_range_for_images[dim2])

axs[0, 0].scatter(f_z_init_mean(np.array([X[X_index,:]]))[0, dim1], f_z_init_mean(np.array([X[X_index,:]]))[0, dim2], c='black', s=20)

plt.show()

[-0.33979711  0.08615533]
[ 0.21540575 -0.08772666]
[ 0.28721127  0.19133036]
[ 0.58926553  0.0274621 ]
[ 0.92678005 -0.37465519]
[ 1.74048066  1.53533685]
[ 1.75768769  1.7847749 ]
[ 1.98841321  2.08771777]
[ 2.02686715  1.8449111 ]
[ 0.  0.]

Evolution of a single sample

np.random.seed(1)

velocity_noise = np.random.normal(size=(m.n_hmc_steps, 1, m.n_latent)).astype('float32')
single_X = np.array([X[X_index, :]])

init_pos = f_z_init_mean(single_X)  # + np.array([0.0, 0.023]).astype('float32')
init_vel = f_kin_energy_sample_from_noise(single_X, velocity_noise[0])

num_vels_per_hmc = (m.n_lf_steps + 2)
position_array = np.zeros((m.n_hmc_steps * m.n_lf_steps + 1, m.n_latent))
position_array[0] = init_pos
velocity_array = np.zeros((m.n_hmc_steps * num_vels_per_hmc, m.n_latent))
velocity_array[0] = init_vel

for hmc_num in range(m.n_hmc_steps):
    if hmc_num == 0:
        curr_pos = init_pos
        curr_vel = init_vel
    else:
        curr_vel = f_updated_vel_from_noise(single_X, curr_vel, velocity_noise[hmc_num])
        velocity_array[hmc_num * (m.n_lf_steps + 2)] = curr_vel
    
    lf_step_results = f_perform_lf_steps(single_X, curr_pos, curr_vel)
    pos_steps = lf_step_results[:m.n_lf_steps]
    vel_half_steps_and_final = lf_step_results[m.n_lf_steps:]
    final_vel = lf_step_results[-1]
    final_pos = pos_steps[-1]
    
    position_array[hmc_num * m.n_lf_steps + 1: (hmc_num + 1)*m.n_lf_steps + 1] = pos_steps[:, 0, :]
    velocity_array[hmc_num * num_vels_per_hmc + 1: (hmc_num + 1) * num_vels_per_hmc] = vel_half_steps_and_final[:, 0, :]
    
    curr_pos = final_pos
    curr_vel = final_vel

fig, axs = plt.subplots(1, 2, figsize=(18, 9))
step_color = cm.jet(np.linspace(0, 1, position_array.shape[0]))
CS = axs[0].contour(x, y, pot_energy_matrix, contour_levels)
CS_vel = axs[1].contour(kin_x, kin_y, kin_energy_matrix, vel_contour_levels)
hmc_step_indices = np.arange(0, position_array.shape[0], m.n_lf_steps)
size_array = 40*np.ones((position_array.shape[0],))
size_array[hmc_step_indices] = 100
axs[0].scatter(position_array[:, dim1], position_array[:, dim2], c=step_color, lw=1, s=size_array)
axs[1].set_color_cycle(step_color)

for hmc_num in range(m.n_hmc_steps):
    curr_vel_range = np.arange(num_vels_per_hmc * hmc_num, num_vels_per_hmc * (hmc_num + 1) - 2)
    init_vel_ind = hmc_num * num_vels_per_hmc
    final_vel_ind = (hmc_num + 1) * num_vels_per_hmc - 1
    curr_index = hmc_step_indices[hmc_num]
    next_index = hmc_step_indices[hmc_num + 1]
    for j in curr_vel_range:
        axs[1].plot(velocity_array[j:j+2, dim1], velocity_array[j:j+2, dim2], lw=2)
    axs[1].scatter(velocity_array[init_vel_ind, dim1], velocity_array[init_vel_ind, dim2], c=step_color[curr_index], lw=0, s=100)
    axs[1].scatter(velocity_array[final_vel_ind, dim1], velocity_array[final_vel_ind, dim2], c=step_color[next_index], lw=0, s=100)

for hmc_num in range(m.n_hmc_steps):
    final_vel_ind = (hmc_num + 1) * num_vels_per_hmc - 1
    next_index = hmc_step_indices[hmc_num + 1]
    axs[1].plot(velocity_array[final_vel_ind-1:final_vel_ind+1, dim1], velocity_array[final_vel_ind-1:final_vel_ind+1, dim2], lw=2, c=step_color[next_index])

Auxiliary model for the final velocity

variation_start = z_sample_final_mean - 2*z_sample_final_std
variation_end = z_sample_final_mean + 2*z_sample_final_std

final_vel_model_mean_output = np.zeros((m.n_latent, num_repeats, m.n_latent))
final_vel_model_var_output = np.zeros((m.n_latent, num_repeats, m.n_latent))

for variation_dim in range(m.n_latent):
    z_variation = np.linspace(variation_start[variation_dim], variation_end[variation_dim], num_repeats)
    sample_array = np.tile(z_sample_final_mean, (num_repeats, 1))
    sample_array[:, variation_dim] = z_variation
    final_vel_model_mean_output[variation_dim] = f_v_final_mean(repeated_X, sample_array)
    final_vel_model_var_output[variation_dim] = f_v_final_var(repeated_X, sample_array)

fig, axs = plt.subplots(1, 2, figsize=(18, 9))
axs[0].scatter(final_vel_model_mean_output[:, :, dim1], 
           final_vel_model_mean_output[:, :, dim2],  
           c=np.transpose(np.tile(np.linspace(0,m.n_latent-1,m.n_latent), (num_repeats, 1))), 
           lw=0, s=5)
axs[1].scatter(final_vel_model_var_output[:, :, dim1], 
           final_vel_model_var_output[:, :, dim2],  
           c=np.transpose(np.tile(np.linspace(0,m.n_latent-1,m.n_latent), (num_repeats, 1))), 
           lw=0, s=5)

plt.show()

final_vel_mean = f_v_final_mean(repeated_X, z_samples[3, :, :])
final_vel_var = f_v_final_var(repeated_X, z_samples[3, :, :])
final_vel_nll = f_v_final_model_nll(repeated_X, z_samples[3, :, :], v_samples[3, :, :])

Old snippets

fig, axs = plt.subplots(4, 2, figsize=(18, 36))
# TODO: Analysis of how final_vel_mean and final_vel_var depend on z (since they all share the same x)

print z_samples[3, :, :].mean(axis=0)
print z_samples[3, :, :].var(axis=0)
print v_samples[3, :, :].mean(axis=0)
print v_samples[3, :, :].var(axis=0)
print f_v_init_var(np.array([X[X_index, :]]))

print final_vel_nll.mean()
plt.boxplot(final_vel_nll, whis=1)
plt.show()

centers = np.zeros((10,n_latents))
stddevs = np.zeros((10,n_latents))
centers_init = np.zeros((10,n_latents))
stddevs_init = np.zeros((10,n_latents))
for i in range(10):
    Li = f_z_sample(X[Z.argmax(1) == i])
    centers[i] = Li.mean(axis=0)
    stddevs[i] = np.std(Li, axis=0)
    
    Li_init = f_z_init_sample(X[Z.argmax(1) == i])
    centers_init[i] = Li_init.mean(axis=0)
    stddevs_init[i] = np.std(Li_init, axis=0)

fig, axs = plt.subplots(1, 2, figsize=(18, 9))
axs[0].scatter(centers[:, dim1], centers[:, dim2], c=range(10), s=50)
axs[0].scatter(centers_init[:, dim1], centers_init[:, dim2], c=range(10), s=50, marker=u's')

axs[1].scatter(centers[:, dim1], centers[:, dim2], c=range(10), s=50)
axs[1].scatter(centers[:, dim1] + stddevs[:, dim1], centers[:, dim2], c=range(10), s=50, marker=u'>')
axs[1].scatter(centers[:, dim1] - stddevs[:, dim1], centers[:, dim2], c=range(10), s=50, marker=u'<')
axs[1].scatter(centers[:, dim1], centers[:, dim2] + stddevs[:, dim2], c=range(10), s=50, marker=u'^')
axs[1].scatter(centers[:, dim1], centers[:, dim2] - stddevs[:, dim2], c=range(10), s=50, marker=u'v')

#axs[0].set_xlim(-1.2, 1.2)
#axs[0].set_ylim(-1.2, 1.2)
#axs[1].set_xlim(-1.2, 1.2)
#axs[1].set_ylim(-1.2, 1.2)

print (centers[:, dim1] - centers_init[:, dim1])
print (centers[:, dim2] - centers_init[:, dim2])
print (stddevs[:, dim1] - stddevs_init[:, dim1])
print (stddevs[:, dim2] - stddevs_init[:, dim2])